Digital Root

[graham7755]

Don't all jump down my neck at once; I'm not a scientist. I appreciate how this kind of stuff, rightly or wrongly, might appear basic, all the same it's raised my curiosity. I was surprised to find a pattern created by the digital root of the platonic solid numbers.

 

Example;

 

Tetrahedral Number - 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, etc

 

The digital root of the above sequence expressed in rows of nine.

 

4 1 2 8 2 3 3 3 4

7 4 5 2 5 6 6 6 7

1 7 8 5 8 9 9 9 1

 

Now taking the digital root of the first three numbers, i.e., (412 = 7) and by doing the same with each consecutive three grouping, a repetitive pattern of, - 741 - 741 - 741 begins to emerge.

 

The sequence repeats after 27 places. It uses each number three times, and in the vertical column numerical sequence's from other shapes can be seen, i.e., - 471 for the Square-Pyramid, and 258 for the Icosahedron.

 

With the exception of the cube, which produces a repetitive sequence of 8 9 1, and the dodecahedron, repeating a cycle after nine places, the other shapes highlight the 27 digit cycle, which may well go on for ever.

 

I would be interested to hear comments, and whether or not anybody is familiar with any author's papers, or books, on this matter.